### Abstract

We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.

Original language | English |
---|---|

Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Probability Theory and Related Fields |

Volume | 84 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1990 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

*Probability Theory and Related Fields*,

*84*(1), 1-26. https://doi.org/10.1007/BF01288555

**Self-avoiding paths on the pre-Sierpinski gasket.** / Hattori, Kumiko; Hattori, Tetsuya; Kusuoka, Shigeo.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 84, no. 1, pp. 1-26. https://doi.org/10.1007/BF01288555

}

TY - JOUR

T1 - Self-avoiding paths on the pre-Sierpinski gasket

AU - Hattori, Kumiko

AU - Hattori, Tetsuya

AU - Kusuoka, Shigeo

PY - 1990/3

Y1 - 1990/3

N2 - We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.

AB - We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.

UR - http://www.scopus.com/inward/record.url?scp=0013244978&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013244978&partnerID=8YFLogxK

U2 - 10.1007/BF01288555

DO - 10.1007/BF01288555

M3 - Article

AN - SCOPUS:0013244978

VL - 84

SP - 1

EP - 26

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1

ER -